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x^2-76x+513=0
a = 1; b = -76; c = +513;
Δ = b2-4ac
Δ = -762-4·1·513
Δ = 3724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3724}=\sqrt{196*19}=\sqrt{196}*\sqrt{19}=14\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-14\sqrt{19}}{2*1}=\frac{76-14\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+14\sqrt{19}}{2*1}=\frac{76+14\sqrt{19}}{2} $
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